Bootstrapping Gini

Income inequality in the Philippines, as measured by the Gini coefficient, declined from 46.05 to 44.84 between 2003 and 2009.[1] Is the observed difference in the the Gini coefficient a real reduction in inequality in income distribution or is it only due to sampling variations?

A friend asked me a question related to this weeks ago. She asked if I know a Stata command that tests the significance between the difference of two Gini coefficients. Lazy to think about it, I just shrug the problem with a ‘no’ and never bothered to search for a solution. This problem came back to me while reading the bootstrapping section of NetCourse 151–Lecture 3. Indeed, when I searched further, a number of literature have used bootstrapping for this purpose. Examples include Mills and Zandvakili (1997) and Biewen (2002).[2][3]

Using Stephen Jenkins’s -ineqdeco- (“ssc install ineqdeco”) to calculate for the Gini coefficients, I did the following bootstrapping exercise for a hypothetical dataset:

/* Program to calculate difference in Gini coefficients */
cap program  drop ginidiff
program ginidiff, rclass
qui ineqdeco income if year == 1
return scalar gini1 = r(gini)
qui ineqdeco income if year == 2
return scalar gini2 = r(gini)
return scalar diff = return(gini1) – return(gini2)

/* Generate hypothetical dataset /
set obs 200
gen year = 1 in 1/100
replace year = 2 in 101/200
set seed 56453
gen income = runiform()
1000 if year == 1
set seed 86443
replace income = runiform()*1000 if year == 2

/* Apply bootstrap /
assert income < .    /
Make sure no missing values */
set seed 873023
bootstrap r(diff), reps(1000) nodots : ginidiff

program drop ginidiff

Whether this straightforward application of bootstrapping is the best solution is another story (and the more important one). For a discussion of other proposed methods and of the limitations of bootstrapping in this context, see for example, Palmitesta, P. et al (2000) and Van Kerm (2002).[4][5]

[1] Thanks to Shiel Velarde (World Bank Manila) for the Gini estimates. These numbers are based on the Family Income and Expenditure Survey (FIES).

[2] Mills, J. and Zandvakili, S. (1997). “Statistical Inference via Bootstrapping for Measures of Inequality”. Journal of Applied Econometrics 12 (2): 133–150. (Working Paper version can be downloaded here)

[3] Biewen, M. (2002). “Bootsrap inference for inequality, mobility and poverty measurement.” Journal of Econometrics 108 (2002): 317–342.

[4] Palmitesta, P. et al (2000). “Confidence Interval Estimation for Inequality Indices of the Gini Family.” Computational Economics

[5] Van Kerm, P. (2002). “Inference on inequality measures: A Monte Carlo experiment.” Journal of Economics 9(Supplement1): 283-306. (Working Paper version can be downloaded here)